Inverse Problems and Parameter Estimation (GEOS 627)
University of Alaska Fairbanks
Carl Tape

Syllabus

Prerequisites:
Calculus III (MATH 202), Linear Algebra (MATH 314)

Textbooks:
1. Parameter Estimation and Inverse Problems
Aster, Borchers, Thurber, 2nd ed., 2013
2. Inverse Problem Theory and Methods for Model Parameter Estimation
Tarantola, 2005

Additional resources: https://github.com/uafseismo/classes

Problem Sets

Problem Set
background reading
file tag
download
1
Matrix operations and decompositions Aster App. A
math
pdf
2
Introduction to inverse problems Aster Ch. 1
ch1
pdf
3
Probabilistic inversion for earthquake epicenter
Tarantola 7.1, Ch. 2
epi
pdf
4
Covariance functions and Gaussian random fields
Tarantola 5.1-5.3, Aster App. B
cov
pdf
5
Iterative methods with generalized least squares
Tarantola 6.22, Ch. 3
iter
pdf
6
Statistical aspects of least squares
Aster Ch. 2
ch2
pdf
7
Truncated singular value decomposition
Aster Ch. 3
grav
pdf
8
Estimation of magmatic source for InSAR interferogram
remote sensing papers
mogi
pdf






Labs
Lab
file tag
download
Fitting a line to scattered data
linefit
pdf
The rejection method of generating samples (associated with PS#3)
sampling
pdf
Samples of a covariance matrix
cov
pdf
Iterative Newton method
newton
pdf
Earthquake location with generalized least squares
iter
pdf
Geometry of singular value decomposition
svdgeom
pdf
SVD approach to ballistic problem
svdball
pdf
Aster Chapters 2 and 3 examples
ch2
pdf
Singular value spectra
svdspec
pdf
Estimation of magmatic source for InSAR interferogram mogi
pdf
Principal component analysis pca
pdf

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